Re: information content of measures (fwd)

From: Wei Dai <weidai.domain.name.hidden>
Date: Sun, 10 Jan 1999 15:13:46 -0800

On Mon, Jan 11, 1999 at 09:53:44AM +1100, Russell Standish wrote:
> It would certainly help to define some terms - what do you
> mean by B* (powerset of B? set of all binary strings?) What exactly is
> a universal prefix machine? Can it be any map from B* to N?

As I said, the notation is from Li and Vitanyi. B* is the set of all
finite binary strings. A universal prefix machine is a kind of universal
Turing machine where no program is a prefix of another.

> > U'(u)(x) = \sum_{U(p)=x}u(p)
>
> This definition doesn't even parse. U' is defined over the set of
> universal prefix machines, not (something) x N. What is u? And what is
> the index that the sum is performed over - {p:U(p)=x}, or is it
> {U:U(p)=x}? In any case the independent variable ought to appear on
> the RHS.

U' is not defined over the set of universal prefix machines, it's defined
over the set of measures on infinite binary strings. Since I already
specified U is some particular universal prefix machine, the only
available index is p.

> I think I'd better bail at this point, pending clarification.

Hope that helps.
Received on Sun Jan 10 1999 - 15:16:25 PST